二进制运算

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

Let us look at parallels between arithmetic using binary numbers and arithmetic using decimal numbers.

我们采用与十进制运算对比的办法来介绍二进制数的运算方法。

Where noted, each type may have a special interpretation of a binary arithmetic operator.

每一个类可能有一个具体的二进制运算符号。

In ''.'binary'.'' arithmetic, a complementation process where all the1's in a ''.

二进制运算中的一种求反过程，在这种过程中，二进制''。

In binary arithmetic, a complementation process where all the1's in a binary number are changed to0's and vice versa.

二进制运算中的一种求反过程，在这种过程中，二进制数中的所有1都变换成0，所有的0都变换成1。

The first generation of computer was characterized by the most prominent feature of the ENIAC-vacuum tubes.Through 1950,several other notable computers were built,each contributing significant advancement,such as binary arithmetic,random access,and the concept of stored programs.These computer concepts are common in today's computers.

第一代计算机ENIAC以真空管为显著标志，到1950年又制造出了另外几台著名的计算机，而且每一台都取得了很大的进展，如像二进制运算、随机存取和存储程序的概念，这些概念在当今的计算机中仍是普遍使用的。

Based on an analysis of the internal relation between binary and sets ,a novel idea of binary-based set operation is presented in this paper.

通过比较二进制与集合之间的内在联系，提出了基于二进制的集合运算思想，给出了基于二进制的各种集合运算算法，该算法有效解决了传统集合操作算法中运算速度慢，效率低的不足，并提供了求幂集，交集，并集等集合运算算法的c语言源程序。

And several rough set operation algorithms are also offered in this paper,such as upper approximation set,lower approximation set,intersection, cardinal number and so on.

通过讨论二进制与粗糙集之间的内在联系，提出基于二进制的粗糙集运算理论，并借助二进制的位运算操作，给出粗糙集的上近似集和下近似集、等价类的交、集合的基数的运算算法。

In computing , most significant bit is the bit position in a binary number having the greatest value. The msb is sometimes referred to as the left-most bit , due to the convention in positional notation of writing more significant digits further to the left.

在计算机运算中，最高有效位，是指在一个二进制数中具有最大值的那一个二进制位。msb有时也被称为"最左边的位"，这是因为在权位记数法中习惯上将较大的有效数字顺序的写在左边。

In the absence of the chairman, his deputy take the chair

二进制运算中的一种求反过程，在这种过程中，二进制数中的所有1都变换成0，所有的0都变换成1。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。